BENFIELD GREIG

1. Long Term Reinsurance Buying Strategies modelled using a component based DFA Tool Astin July 2001 BENFIELD GREIG

2. Introduction Investigate possible reinsurance strategies over several years. Two Strategies: • Constant Cover, but vary premium spend. • Constant Spend, but vary cover purchased. Use Monte Carlo Simulation to evaluate Risk / Return for an example company.

3. Reinsurance Pricing Factors • Many potential ways to model changes in reinsurance pricing • Various factors including: • Loss Experience • Changes in exposure • Reinsurance Market conditions • The method used here is based on Loss Experience, with exposure and market factors assumed to be constant.

4. Example Company Example model is a property Cat XL programme with the following parameters (USD million): • Premium Income 120 • Expenses 30 • Small Claims 48 • Large Cat Loss Freq Poisson distribution with mean 1. • Large Cat Loss Size Lognormal distribution, mean 12, standard dev. 16.

5. Example Company Reinsurance • The reinsurance programme consists of 4 layers as follows: • (USD million) • All layers have 1 reinstatement at 100%. • Initial coinsurance for all layers is 25%.

6. Different Strategies • Each Layer considered Separately • In Constant Cover strategies, coinsurance is fixed and premium paid varies. • In Constant Spend strategies, coinsurance varies to keep premium spend constant.

7. Change in Reinsurance Pricing • The price of each layer in the reinsurance programme will vary, with an increase in price if the experience account (EA) for the layer is negative, and a reduction in price if the EA is positive and there are no losses in the previous year. • EA = reinsurance premiums and reinstatements – recoveries • if EA < 0 then premium = previous premium + EA * 10% • if EA > 0 then rate = previous rate * 90% • Initial EA = 0.

9. Model Implentation • Modelled Using ReMetrica II • Component Based Framework for risk analysis and DFA ( Dynamic Financial Analysis ) • Main Uses Include: • Reinsurance Pricing and Strategy • Risk Based Capital Modelling & Capital Allocation • Business Planning

10. The Model

11. Results • The graphs below show the cedant’s net underwriting result. As a measure of risk we show: • Standard Deviation • 1 in 100 result • Probability of a negative UW result • As a measure of return we use expected UW result. • The numbers on the graph indicate the years 1 – 5.

12. Results • The results were based on 20,000 simulations using stratified sampling of 10,000 strata • Performed sensitivity testing with further simulations ( 50,000 ) and different parameters.

13. Risk Return - Standard Deviation

14. Risk Return - 1 in 100

15. Risk Return - Probability Loss

16. Conclusions • Constant Spend strategy better than Constant Cover Strategy. • Return appears similar, but risk is less. • Consistent across different risk measures.

17. Relevance • Constant Spend strategy is similar to the following strategy: • Buy core programme down from a top PML ( probable maximum loss ) figure and buy lower down on an opportunistic basis. • Opposite strategy reduces reinsurance when cost is low and buys more when costs are high. I call this the ‘short memory’ strategy. • Constant Cover is neutral. • This analysis indicates that buying down from your PML as far as your budget will allow is a good strategy. ( In practice, will still need a core programme. ) • This analysis may help a reinsurance manager defend against the ‘short memory’ strategy.